Simulation is Real

Computer simulations of complex processes have always been connected with the real world. Analog computation was invented to solve a problem in the real world. The best known early model of a biological system showed that a computer would be necessary to study real systems. Now that computation power is abundant, the complexity of simulations has risen to provide realism. Connections with the real world are essential in testing the simulation. Also, models are now too large for exhaustive testing, so the researcher has to fall back on the same approach used in investigating the real world: carefully planned experiments

Sodium-Calcium Exchange: Derivation of a State Diagram and Rate Constants from Experimental Data

A mechanism is developed for Na+-Ca2+ exchange using a new approach made possible by the availability of computer software that allows the systematic search of a large parameter space for optimum sets of parameters to fit multiple sets of experimental data. The approach was to make the experimental data dictate the form of the mechanism: the qualitative features of the data dictating the number and nature of the states of the exchanger and their interrelationship, and the quantitative aspects of the data dictating the values of the rate constants that govern the amount of each state relative to the total amount of exchanger. A single set of experimental data served this initial purpose, namely, observations of equilibrium Ca2+-Ca2+ exchange in cardiac sarcolemmal vesicles (Slaughter et al., 1983, J. biol. Chem. 258, 3183-3190). From this data a minimum mechanism was induced having 56 states (SYM56), which gave satisfactory quantitative fits to the experimental data. With this set of parameters additional experimental data were fitted, from the same preparation, the single cardiac cell and the squid giant axon, with some changes in parameters, but none dramatic. In spite of the symmetric nature of the mechanism, i.e. binding constants for Na+ and Ca2+ do not depend on the orientation of the binding sites, the mechanism exhibits marked asymmetric behavior similar to that observed experimentally. Finally, in accounting for Ca2+-Ca2+ exchange in the absence of monovalent cations, Ca2+ influx becomes dependent on intracellular Ca2+-an unexpected outcome-exactly in keeping with the essential activator role of intracellular Ca2+ observed by DiPolo & Beaugé (1987, J. gen. Physiol. 90, 505-525). Observations of Na+-Ca2+ exchange in the retinal rod outer segment are well fitted with a simplified version of SYM56 comprising 25 states (namely, SYM25), supporting the notion that the exchanger in the retinal rod outer segment differs from that in cardiac sarcolemma and squid axon. Maximum turnover rate of 840 sec-1 for SYM56 and 20 sec-1 for SYM25 are comparable to those reported for the exchanger in cardiac muscle and retinal rod outer segment, respectively. © 1992 Academic Press Limited

Slow Conduction in Cardiac Muscle: A Biophysical Model

Mechanisms of slow conduction in cardiac muscle are categorized and the most likely identified. Propagating action potentials were obtained experimentally from a synthetically grown strand of cardiac muscle (around 50 μm by 30 mm) and theoretically from a one-dimensional cable model that incorporated varying axial resistance and membrane properties along its length. Action potentials propagated at about 0.3 m/s, but in some synthetic strands there were regions (approximately 100 μm in length) where the velocity decreased to 0.002 m/s. The electrophysiological behavior associated with this slow conduction was similar to that associated with slow conduction in naturally occurring cardiac muscle (notches, Wenckebach phenomena, and block). Theoretically, reasonable changes in specific membrane capacitance, membrane activity, and various changes in geometry were insufficient to account for the observed slow conduction velocities. Conduction velocities as low as 0.009 m/s, however, could be obtained by increasing the resistance (r(i)) of connections between the cells in the cable; velocities as low as 0.0005 m/s could be obtained by a further increase in r(i) made possible by a reduction in membrane activity by one-fourth, which in itself decreased conduction velocity by only a factor of 1/1.4. As a result of these findings, several of the mechanisms that have been postulated, previously, are shown to be incapable of accounting for delays such as those which occur in the synthetic strand as well as in the atrioventricular (VA) node